Exponents

The exponent 3 means that 4 is multiplied by itself three times: \(4^3=4\times4\times4=64\). Therefore, 64 is correct. The value 16 is \(4^2\), so it is a close but incorrect option. Exam tip: In \(a^n\), n tells how many times a is used as a factor.

Any non-zero number raised to the power 0 equals 1. Therefore, \(5^0=1\). Choosing 0 is a common error from applying exponent rules incorrectly; here the base, 5, is non-zero. Exam tip: remember that \(a^0=1\) only when \(a\ne0\).

An exponent of 2 means multiplying 7 by itself: \(7^2 = 7 \times 7 = 49\). Therefore, 49 is the correct answer. The value 14 comes from \(7+7\), not from squaring 7. Exam tip: Rewrite \(a^2\) as \(a \times a\) before calculating.

An exponent of 5 means that 2 is multiplied by itself five times: \(2^5 = 2 \times 2 \times 2 \times 2 \times 2 = 32\). Therefore, 32 is the correct option. 16 is \(2^4\), while 64 is \(2^6\). Exam tip: each successive power of 2 is double the preceding power.

When powers with the same base are multiplied, their exponents are added: \(3^2\times 3^1=3^{2+1}=3^3=27\). Therefore, 27 is correct. \(9\) is only the value of \(3^2\), whereas \(81\) equals \(3^4\). Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

An exponent of 2 means that 11 is multiplied by itself: \(11^2 = 11 \times 11 = 121\). Therefore, 121 is the correct answer. 111 is not the square of 11. Exam tip: To find a square, multiply the number by itself.

Here, \(12^2\) means the square of 12, that is, \(12 \times 12\). Since \(12 \times 12 = 144\), the correct answer is 144. A number such as 132 is not obtained by squaring 12. Exam tip: Read \(n^2\) as \(n \times n\) before multiplying.

For any non-zero number, the zero-exponent rule is \(a^0=1\). Therefore, \(1^0=1\). Option 0 is not correct; \(0^0\) is generally treated as undefined/indeterminate, but the base here is 1. Exam tip: Do not write 0 merely because the exponent is 0.

Here, 2 is multiplied by itself 6 times: \(2^6=2\times2\times2\times2\times2\times2=64\). Therefore, 64 is correct. The nearby distractor 32 equals \(2^5\), not \(2^6\). Exam tip: an exponent \(n\) tells how many times the base is used as a factor.

An exponent of 2 means that 13 is multiplied by itself: \(13^2 = 13 \times 13 = 169\). Therefore, 169 is the correct option. Note that 143 equals \(13 \times 11\), not the square of 13. Exam tip: to find a square, multiply the number by itself.

An exponent of 2 means multiplying 15 by itself: \(15^2 = 15 \times 15 = 225\). Therefore, 225 is the correct answer. 215 is not the square of 15. Exam tip: To find the square of a number, multiply the number by itself.

When powers with the same base are multiplied, their exponents are added: \(2^1\times2^2=2^{1+2}=2^3=8\). Therefore, the correct answer is 8. The value 4 is only \(2^2\), so it is not correct. Exam tip: use \(a^m\times a^n=a^{m+n}\) only when the bases are the same.

An exponent of 2 means multiplying 14 by itself: \(14^2 = 14 \times 14 = 196\). Therefore, 196 is the correct option. 144 is a close distractor because it equals \(12^2\), not \(14^2\). Exam tip: To find a square, multiply the number by itself.

The exponent 4 means that 3 is multiplied by itself four times: \(3^4=3\times3\times3\times3=81\). Therefore, 81 is the correct answer. The value 27 is \(3^3\), so it is a close but incorrect option. Exam tip: In \(a^n\), n tells how many times a is used as a factor.

In an exponent, 16^2 means multiplying 16 by itself: 16 \times 16 = 256. Therefore, the correct answer is 256. The value 196 is 14^2, not 16^2. Exam tip: To find the square of a number, multiply the number by itself.

Any number raised to the power 1 equals the number itself: \(a^1=a\). Therefore, \(9^1=9\). The value 81 is \(9^2\), so it is not correct here. Exam tip: when the exponent is 1, write the base directly.

The square of a number is found by multiplying the number by itself. Thus, \(18^2 = 18 \times 18 = 324\), so 324 is correct. 288 is not the square of 18. Exam tip: You can also check \(18^2\) using \((20-2)^2\).

In \(5^3\), 5 is the base and 3 is the exponent. It means \(5\times5\times5=125\), so 125 is the correct option. The value 25 is \(5^2\), not \(5^3\). Exam tip: in \(a^n\), multiply the base \(a\) by itself \(n\) times.

\(2^7\) means multiplying 2 by itself seven times: \(2\times2\times2\times2\times2\times2\times2=128\). Therefore, the correct answer is 128. The value 64 is \(2^6\), so it is a close but incorrect option. Exam tip: each successive power of 2 is double the preceding power.

To find the square of a number, multiply it by itself. Thus, \(20^2=20\times20=400\), so 400 is correct. The value 200 is obtained by multiplying 20 by 10, not by squaring it. Exam tip: \(a^2\) always means \(a\times a\).